{"id":"https://openalex.org/W2961955365","doi":"https://doi.org/10.1007/s11760-019-01514-4","title":"The Biharmonic Eigenface","display_name":"The Biharmonic Eigenface","publication_year":2019,"publication_date":"2019-06-07","ids":{"openalex":"https://openalex.org/W2961955365","doi":"https://doi.org/10.1007/s11760-019-01514-4","mag":"2961955365"},"language":"en","primary_location":{"id":"doi:10.1007/s11760-019-01514-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11760-019-01514-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11760-019-01514-4.pdf","source":{"id":"https://openalex.org/S156904493","display_name":"Signal Image and Video Processing","issn_l":"1863-1703","issn":["1863-1703","1863-1711"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Signal, Image and Video Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11760-019-01514-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046076979","display_name":"Ali Ahmed Elmahmudi","orcid":"https://orcid.org/0000-0001-5063-857X"},"institutions":[{"id":"https://openalex.org/I139894009","display_name":"University of Bradford","ror":"https://ror.org/00vs8d940","country_code":"GB","type":"education","lineage":["https://openalex.org/I139894009"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ali Elmahmudi","raw_affiliation_strings":["Centre for Visual Computing, School of Engineering and Informatics, University of Bradford, Bradford, BD7 1DP, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Visual Computing, School of Engineering and Informatics, University of Bradford, Bradford, BD7 1DP, UK","institution_ids":["https://openalex.org/I139894009"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083781406","display_name":"Hassan Ugail","orcid":"https://orcid.org/0000-0002-3084-1797"},"institutions":[{"id":"https://openalex.org/I139894009","display_name":"University of Bradford","ror":"https://ror.org/00vs8d940","country_code":"GB","type":"education","lineage":["https://openalex.org/I139894009"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Hassan Ugail","raw_affiliation_strings":["Centre for Visual Computing, School of Engineering and Informatics, University of Bradford, Bradford, BD7 1DP, UK"],"raw_orcid":"https://orcid.org/0000-0002-3084-1797","affiliations":[{"raw_affiliation_string":"Centre for Visual Computing, School of Engineering and Informatics, University of Bradford, Bradford, BD7 1DP, UK","institution_ids":["https://openalex.org/I139894009"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083781406"],"corresponding_institution_ids":["https://openalex.org/I139894009"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.7111,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.74980318,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"8","first_page":"1639","last_page":"1647"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11448","display_name":"Face recognition and analysis","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/biharmonic-equation","display_name":"Biharmonic equation","score":0.8582513332366943},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.8215997219085693},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.7890981435775757},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.6569961905479431},{"id":"https://openalex.org/keywords/facial-recognition-system","display_name":"Facial recognition system","score":0.6435890197753906},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6370444297790527},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6302836537361145},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.6250436902046204},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5933375358581543},{"id":"https://openalex.org/keywords/word-error-rate","display_name":"Word error rate","score":0.5177145004272461},{"id":"https://openalex.org/keywords/eigenface","display_name":"Eigenface","score":0.4905802309513092},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30572646856307983}],"concepts":[{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.8582513332366943},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.8215997219085693},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.7890981435775757},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.6569961905479431},{"id":"https://openalex.org/C31510193","wikidata":"https://www.wikidata.org/wiki/Q1192553","display_name":"Facial recognition system","level":3,"score":0.6435890197753906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6370444297790527},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6302836537361145},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.6250436902046204},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5933375358581543},{"id":"https://openalex.org/C40969351","wikidata":"https://www.wikidata.org/wiki/Q3516228","display_name":"Word error rate","level":2,"score":0.5177145004272461},{"id":"https://openalex.org/C104906051","wikidata":"https://www.wikidata.org/wiki/Q29695","display_name":"Eigenface","level":4,"score":0.4905802309513092},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30572646856307983},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11760-019-01514-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11760-019-01514-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11760-019-01514-4.pdf","source":{"id":"https://openalex.org/S156904493","display_name":"Signal Image and Video Processing","issn_l":"1863-1703","issn":["1863-1703","1863-1711"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Signal, Image and Video Processing","raw_type":"journal-article"},{"id":"pmh:oai:bradscholars.brad.ac.uk:10454/18901","is_oa":true,"landing_page_url":"http://hdl.handle.net/10454/18901","pdf_url":null,"source":{"id":"https://openalex.org/S4306401846","display_name":"Bradford Scholars (University of Bradford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139894009","host_organization_name":"University of Bradford","host_organization_lineage":["https://openalex.org/I139894009"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"Published version"}],"best_oa_location":{"id":"doi:10.1007/s11760-019-01514-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11760-019-01514-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11760-019-01514-4.pdf","source":{"id":"https://openalex.org/S156904493","display_name":"Signal Image and Video Processing","issn_l":"1863-1703","issn":["1863-1703","1863-1711"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Signal, Image and Video Processing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G150483041","display_name":"PDE-based geometric modelling, image processing, and shape reconstruction","funder_award_id":"778035","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8694499402","display_name":null,"funder_award_id":"778035","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2961955365.pdf","grobid_xml":"https://content.openalex.org/works/W2961955365.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W195533127","https://openalex.org/W391578156","https://openalex.org/W1665704742","https://openalex.org/W1976137296","https://openalex.org/W1985258161","https://openalex.org/W2012474721","https://openalex.org/W2014565677","https://openalex.org/W2036949426","https://openalex.org/W2043694524","https://openalex.org/W2049056913","https://openalex.org/W2055191956","https://openalex.org/W2070851600","https://openalex.org/W2075282432","https://openalex.org/W2088119458","https://openalex.org/W2098693229","https://openalex.org/W2107105977","https://openalex.org/W2109798065","https://openalex.org/W2112739286","https://openalex.org/W2116019577","https://openalex.org/W2137234026","https://openalex.org/W2138451337","https://openalex.org/W2314635033","https://openalex.org/W2325939864","https://openalex.org/W2480304173","https://openalex.org/W2498685805","https://openalex.org/W2547065869","https://openalex.org/W2610857016","https://openalex.org/W2740067724"],"related_works":["https://openalex.org/W1501769554","https://openalex.org/W2000101267","https://openalex.org/W2470527482","https://openalex.org/W2380927352","https://openalex.org/W2147478239","https://openalex.org/W2394274501","https://openalex.org/W2071240963","https://openalex.org/W4200207142","https://openalex.org/W2353697322","https://openalex.org/W3162456779"],"abstract_inverted_index":{"Principal":[0],"component":[1],"analysis":[2],"(PCA)":[3],"is":[4,32],"an":[5,133],"elegant":[6],"mechanism":[7,78],"that":[8,165],"reduces":[9],"the":[10,38,52,61,66,80,85,100,115,120,128,137,154,166,169,185,194],"dimensionality":[11,111],"of":[12,19,25,37,54,65,95,109,122,139],"a":[13,48,71],"dataset":[14],"to":[15,34,51,59,76,88,135,182],"bring":[16],"out":[17,147],"patterns":[18],"interest":[20],"in":[21,103,193],"it.":[22],"The":[23,106,159],"preprocessing":[24,72],"facial":[26],"images":[27,94,108],"for":[28],"efficient":[29],"face":[30,130,183],"recognition":[31,131],"considered":[33],"be":[35],"one":[36],"epitomes":[39],"among":[40],"PCA":[41,55],"applications.":[42],"In":[43,172],"this":[44,77],"paper,":[45],"we":[46,57,90,125,161],"introduce":[47],"novel":[49],"modification":[50],"method":[53,187],"whereby":[56],"propose":[58],"utilise":[60],"inherent":[62,101],"averaging":[63],"ability":[64],"discrete":[67],"Biharmonic":[68,86],"operator":[69,87],"as":[70,79,132],"step.":[73],"We":[74],"refer":[75],"BiPCA.":[81],"Interestingly,":[82],"by":[83],"applying":[84],"images,":[89],"can":[91,112],"generate":[92],"new":[93],"reduced":[96],"size":[97],"while":[98,118],"keeping":[99],"features":[102,121],"them":[104],"intact.":[105],"resulting":[107],"lower":[110],"significantly":[113],"reduce":[114],"computational":[116],"complexities":[117],"preserving":[119],"interest.":[123],"Here,":[124],"have":[126,162],"chosen":[127],"standard":[129],"example":[134],"demonstrate":[136,164],"capacity":[138],"our":[140,174],"proposed":[141],"BiPCA":[142,167,186],"method.":[143],"Experiments":[144],"were":[145],"carried":[146],"on":[148],"three":[149],"publicly":[150],"available":[151],"datasets,":[152],"namely":[153],"ORL,":[155],"Face95":[156],"and":[157],"Face96.":[158],"results":[160],"obtained":[163],"outperforms":[168],"traditional":[170],"PCA.":[171],"fact,":[173],"experiments":[175],"do":[176],"suggest":[177],"that,":[178],"when":[179],"it":[180],"comes":[181],"recognition,":[184],"has":[188],"at":[189],"least":[190],"25%":[191],"improvement":[192],"average":[195],"percentage":[196],"error":[197],"rate.":[198]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}